Numerical simulation of flows from free molecular regime to continuum regime by a DVM with streaming and collision processes

Abstract

A discrete velocity method (DVM) with streaming and collision processes is presented in this work for simulation of flows from free molecular regime to continuum regime. The present scheme can be considered as a semi-Lagrangian like scheme. At first, we follow the conventional DVM to discretize the phase velocity space by a number of discrete velocities. Then, for each discrete velocity, the kinetic equation with BGK-Shakhov model is integrated in space and time within one time step. As a result, a simple algebraic formulation can be obtained, and its solution can be marched in time by the streaming and collision processes. However, differently from the conventional semi-Lagrangian scheme, the present scheme uses the MUSCL approach with van Albada limiter in the process of reconstructing the distribution function at the surrounding points of the cell center, and the transport distance is controlled in order to avoid extrapolation. This makes the present scheme be capable of simulating the hypersonic rarefied flows. In addition, as compared to the unified gas kinetic scheme (UGKS), the present scheme is simpler and easier for implementation. Thus, the computational efficiency can be improved accordingly. To validate the proposed numerical scheme, test examples from free molecular regime to continuum regime are simulated. Numerical results showed that the present scheme can predict the flow properties accurately even for hypersonic rarefied flows.